Person: Castilla González, Elena María
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First Name
Elena María
Last Name
Castilla González
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Estadística e Investigación Operativa
Area
Estadística e Investigación Operativa
Identifiers
5 results
Search Results
Now showing 1 - 5 of 5
Item Robust inference for non-destructive one-shot device testing under step-stress model with exponential lifetimes(2022) Balakrishnan, Narayanaswamy; Castilla González, Elena María; Jaenada Malagón, María; Pardo Llorente, LeandroOne-shot devices analysis involves an extreme case of interval censoring, wherein one can only know whether the failure time is either before or after the test time. Some kind of one-shot devices do not get destroyed when tested, and so can continue within the experiment, providing extra information for inference, if they did not fail before an inspection time. In addition, their reliability can be rapidly estimated via accelerated life tests (ALTs) by running the tests at varying and higher stress levels than working conditions. In particular, step-stress tests allow the experimenter to increase the stress levels at pre-fixed times gradually during the life-testing experiment. The cumulative exposure model is commonly assumed for step-stress models, relating the lifetime distribution of units at one stress level to the lifetime distributions at preceding stress levels. In this paper, we develop robust estimators and Z-type test statistics based on the density power divergence (DPD) for testing linear null hypothesis for non-destructive one-shot devices under the step-stress ALTs with exponential lifetime distribution. We study asymptotic and robustness properties of the estimators and test statistics, yielding point estimation and conffidence intervals for different lifetime characteristic such as reliability, distribution quantiles and mean lifetime of the devices. A simulation study is carried out to assess the performance of the methods of inference developed here and some real-life data sets are analyzed ffinally for illustrative purpose.Item Robust approach for comparing two dependent normal populations through Wald-type tests based on Rényi's pseudodistance estimators(Statistics and Computing, 2022) Castilla González, Elena María; Jaenada Malagón, María; Martín Apaolaza, Nirian; Pardo Llorente, LeandroSince the two seminal papers by Fisher (1915, 1921) were published, the test under a fixed value correlation coefficient null hypothesis for the bivariate normal distribution constitutes an important statistical problem. In the framework of asymptotic robust statistics, it remains being a topic of great interest to be investigated. For this and other tests, focused on paired correlated normal random samples, Rényi's pseudodistance estimators are proposed, their asymptotic distribution is established and an iterative algorithm is provided for their computation. From them the Wald-type test statistics are constructed for different problems of interest and their influence function is theoretically studied. For testing null correlation in different contexts, an extensive simulation study and two real data based examples support the robust properties of our proposal.- Project number: 343
Item Tutoriales guiados de prácticas en “Estadística: Análisis de Datos e Inferencia” mediante el software libre SAS University Edition(2020) Martín Apaolaza, Nirian; Castilla González, Elena María; Chocano Feito, Pedro José; Jaenada Malagón, María; Pardo Llorente, Leandro Item Estimation and Testing on Independent Not Identically Distributed Observations Based on Rényi’s Pseudodistances(IEEE transactions on information theory, 2022) Castilla González, Elena María; Jaenada Malagón, María; Pardo Llorente, LeandroIn real life we often deal with independent but not identically distributed observations (i.n.i.d.o), for which the most well-known statistical model is the multiple linear regression model (MLRM) with non-random covariates. While the classical methods are based on the maximum likelihood estimator (MLE), it is well known its lack of robustness to small deviations from the assumed conditions. In this paper, and based on the Rényi’s pseudodistance (RP), we introduce a new family of estimators in case our information about the unknown parameter is given for i.n.i.d.o.. This family of estimators, let us say minimum RP estimators (as they are obtained by minimizing the RP between the assumed distribution and the empirical distribution of the data), contains the MLE as a particular case and can be applied, among others, to the MLRM with non-random covariates. Based on these estimators, we introduce Wald-type tests for testing simple and composite null hypotheses, as an extension of the classical MLE-based Wald test. Influence functions for the estimators and Wald-type tests are also obtained and analysed. Finally, a simulation study is developed in order to asses the performance of the proposed methods and some real-life data are analysed for illustrative purpose.- Project number: 118
Item Docencia de optimización en el entorno virtual Moodle a partir de ejercicios resueltos(2022) Miranda Menéndez, Pedro; Castilla González, Elena María; Chocano Feito, Pedro José; Jaenada Malagón, María; Martín Apaolaza, Nirian; Martínez Suárez, Susana; Pardo Llorente, LeandroEl presente proyecto trata de mejorar las herramientas que tienen a su disposición los alumnos en el aprendizaje de la asignatura de Optimización. Uno de los problemas a los que se enfrentan los alumnos de esta asignatura es la escasez de bibliografía explícita referente a estos temas. Al ser ya una asignatura muy específica de los estudios de Matemáticas, no hay libros generales que traten estos temas. Por ello, los alumnos están obligados a utilizar un grupo muy reducido de libros de texto. Además, aunque en estos libros se tratan los aspectos teóricos de la asignatura, no contienen una selección de problemas resueltos que permitan a los alumnos evaluar su dominio sobre los algoritmos que aparecen en esta asignatura. Por otra parte, el entorno exam de R se ha desarrollado mucho en los últimos años. En la versión anterior, se podían generar ejercicios de forma aleatoria y a continuación producir un fichero .pdf para su impresión, pensando todavía en un uso en papel. Con la nueva versión del paquete exam todo lo anterior sigue siendo posible pero además permite que estos programas se puedan adecuar a las herramientas online, permitiendo su inclusión como una herramienta en los entornos de enseñanza virtual como Moodle. El objetivo principal de este proyecto es cubrir estas necesidades, de forma que los alumnos cuenten con una herramienta que les permita ejercitarse y profundizar en los aspectos metodológicos de la asignatura a partir de problemas resueltos.